Sufficient condition for reliable logic operations in an over damped bistable system driven by Gaussian white noise

In this paper, we investigate an overdamped bistable system subject to Gaussian white noise and logical inputs. By solving and estimating the steady distribution of the corresponding Fokker–Planck equation and considering the two essential features of the reliable logic operations (RLOs)—initial value independence and sign invariance—we establish the sufficient condition for RLO occurrence and identify parametric resonance phenomena in the system. Our numerical simulations confirm the reliability and accuracy of the theoretical results. This work offers insights into enhancing the accuracy of stochastic systems, particularly in the realm of logical stochastic resonance, thereby contributing to advancements in understanding and controlling stochastic dynamical systems.